A class of steady-state metal-forming problems, with rigid-plastic, incompressible, strain-rate dependent material model and nonlocal Coulomb's friction, is considered. Primal, mixed and penalty variational formulations, containing variational inequalities with nonlinear and nondifferentiable terms, are derived and studied. Existence, uniqueness and convergence results are obtained and shortly presented. A priori finite element error estimates are derived and an algorithm, combining the finite element and secant-modulus methods, is utilized to solve an illustrative extrusion problem.